Toma, S. "Statistics of Steel Weight of Highway Bridges." Bridge Engineering Handbook. Ed. Wai-Fah Chen and Lian Duan Boca Raton: CRC Press, 2000 © 2000 by CRC Press LLC 54 Statistics of Steel Weight of Highway Bridges 54.1 Introduction 54.2 Design Criteria Live Loads • Materials 54.3 Database of Steel Weights 54.4 Statistics of Steel Weights Simply Supported Noncomposite Plate Girder Bridges • Simply Supported Composite Plate Girder Bridges • Simply Supported Box-Girder Bridges • Continuously Supported Plate Girder Bridges • Continuously Supported Box-Girder Bridges • Truss Bridges • Arch Bridges • Rahmen Bridges (Rigid Frames) • Cable-Stayed Bridges 54.5 Regression Equations 54.6 Comparisons Composite and Noncomposite Girders • Simply and Continuously Supported Girders • Framed Bridges • RC Slab and Steel Deck 54.7 Assessment of Bridge Design Deviation • Assessment of Design 54.8 Summary 54.1 Introduction In this chapter, a database of steel highway bridges is formed to assess designs by analyzing them statistically. No two bridges are exact replicas of each other because of the infinite variety of site conditions. Each bridge meets specific soil, traffic, economic, and aesthetics conditions. The struc- tural form, the support conditions, the length, width, and girder spacing, pedestrian lanes, and the materials, all depend on a unique combination of design criteria. Even if the stipulated criteria are identical, the final bridges are not, as they naturally reflect the individual intentions of different designers. Therefore, steel weight is a major interest to engineers. Steel weight of highway bridges is one of the most important of the many factors that influence bridge construction projects. The weight gives a good indication of structural, economic, and safety Shouji Toma Hokkai-Gakuen University, Japan © 2000 by CRC Press LLC features of the bridge. Generally, the weight is expressed by as a force per square unit of road surface area (tonf/m 2 or kN/m 2 ). Stochastic distribution of the weight includes many influential factors to designs that cause scatter. The analysis of this scatter may suggest the characteristics of the bridges. As a general rule, simple bridges are lighter than more complex ones, bridges with high safety margins are heavier, and composite construction results in a lighter bridge overall. A designer thereby gets insight into the characteristics of a bridge. As bridge design also requires the estimate of steel weight in advance, the data collected here are useful. In Japan, many steel bridges have been constructed in the past few decades. The weight of steel used in these bridges has been collected into a single database. The bridges are all Japanese, but engineers from other countries use similar structural and economic considerations and can usefully employ these in their designs. In this chapter, Japanese design criteria are presented first. The live loads and material properties are described in special detail to clarify differences that other countries may note. Then, the computer database is explained and used to make comparisons between plate and box girders, truss and frame bridges, simply supported and continuously supported bridges, reinforced concrete slab deck and steel deck, and more. 54.2 Design Criteria 54.2.1 Live Loads The strength required for a bridge to sustain largely depends on the live load, and the live load generally differs from country to country. Since the weight information used here follows Japanese specifications, those will be the ones explained. The last version of the bridge design specification was published in 1996 [1], and is based on a truck weight of 25 tonf (245 kN). However, the bridges studied here were designed using an old version of the code [2], and thus used a truck load of 20 tonf (196 kN). The 20 t live load (TL-20) takes the two forms shown in Figure 54.1a. The T-load is used to design local components such as the slab or the floor system and the L-load is used for global ones such as the main girders. The T-load is the concentrated wheel loads and the L-load is further subdivided. A partially distributed load (caused by the truck) and a load distributed along the length of the bridge (corresponding to the average traffic load) comprises the L-load. Most of the bridges were designed for TL-20, but on routes, such as those near harbor ports, heavy truck loads are expected and these were designed for TT-43 (Figure 54.1b). In this database the difference is not considered. When a bridge has side lanes for pedestrian traffic, and the live load (the crowd load) is small compared to vehicular traffic loads, usually less steel is required. However, the difference of the weight for pedestrian and vehicular lanes is not considered in this database. The surface area of the sidewalk is considered equally as heavy as the area in the vehicle lanes. 54.2.2 Materials The strength of steel varies widely. A mild steel may have a yield strength of about 235 N/mm 2 and is commonly used in bridge design but higher strengths of 340 or 450 N/mm 2 are also used, often in large bridges. Various strength of steel are considered in this study. Clearly, when higher-strength steels are used, the weight of steel required goes down. However, the difference in strength level of steel is not distinguished in the database. Aa a selection of strength level is made considering rationality of design, it will generally result in similar decisions for many bridges. In other words, similar bridge designs specify similar material strengths. The effect of strength is thus included implicitly in the database. © 2000 by CRC Press LLC FIGURE 54.1 Live load (TL-20). (a) T-Load (W = 20 tf); (b) L-Load; (c) TT-43 (W = 43 tf). © 2000 by CRC Press LLC 54.3 Database of Steel Weights The Japan Association of Steel Bridge Construction (JASBC) publishes an annual report on steel bridge construction [3]. Information about the weight of steel was taken from these reports over a period of 15 years (from 1978 to 1993). The database was collected using a personal computer [4]. The weight was expressed in terms of intensity per unit road surface area (tonf/m 2 ). Table 54.1 shows the quantity of data available for each year relating to various types of bridges. When enough data exist to perform a reliable statistical analysis, new data are used. When the year’s sample is small, all the data are included. The data in Table 54.1 are plotted in Figure 54.2, which also shows the number of steel bridges constructed in Japan. From Figure 54.2, it can be seen that about 500 steel bridges are constructed each year. The tendency of the structural types can also be seen: simply supported composite plate girders are gradually replaced by continuous girders. This can be explained as expansion joints damage the pavement and cause vehicles to make noise as they pass over the joints. 54.4 Statistics of Steel Weights Weight distributions for various types of bridges are shown in Figures 54.3 through 54.13. The weights are plotted against the span length which shows applicable length for the type of bridge. In the figures the mean values are shown by a line and a parabola curve; the equations are given in Table 54.2. 54.4.1 Simply Supported Noncomposite Plate Girder Bridges In Figure 54.3 the distributions for simply supported plate girder bridges with reinforced concrete (RC) slab and steel decks are shown. The steel weight varies considerably, from which one can investigate the peculiarity of the bridge. FIGURE 54.2 Number of highway steel bridge constructions in Japan. TABLE 54.1 Number of Input Data Year Completed Type of Bridge 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 Total Simple plate girder 35 33 22 25 31 34 30 39 28 41 70 49 33 38 39 30 577 Simple plate girder (steel deck) 6254696891112914548118 Simple composite plate girder 266 216 202 174 135 109 121 126 97 100 114 92 75 86 69 61 2043 Simple box girder 30 29 34 24 24 12 29 33 24 36 41 36 35 40 32 44 503 Simple box girder (steel deck) 15 12 6647610165161414212028200 Simple composite box girder 42 36 18 23 9 13 10 13 12 17 21 18 11 8 6 10 267 Continuous plate girder 155 146 95 109 112 118 140 139 139 168 187 172 178 180 147 150 2335 Continuous plate girder (steel deck) 044005666145650254 Continuous box girder 48 44 45 49 50 38 50 46 68 62 65 55 72 104 85 66 947 Continuous box girder (steel deck) 9 18 19 16 11 16 19 24 23 17 25 20 23 27 28 42 337 Simple truss 16 26 15 7 11 16 11 14 9 15 15 10 17 8 10 11 211 Continuous truss 10 13 9 10 0 6 12 8 6 12 7 6 12 5 6 2 124 Langer 19 12 8 12 7 10 7 12 453754811134 Trussed Langer 294522032152414147 Lohse 11 12 12 10 9 11 11 8 19 7 8 11 13 17 17 7 183 Nielsen Lohse 200014424345575753 Rigid frame (Rahmen) 16 12 5 15 3 9 8 10 10 12 17 15 10 8 14 18 182 Rigid frame ( π type) 364644452566768783 Arch bridge ——————————— 2434215 Cable-stayed bridge (steel deck) 002202154524555648 Total 685 630 509 497 419 425 475 511 482 523 622 538 543 578 511 513 8461 © 2000 by CRC Press LLC TABLE 54.2 Coefficients of Regression Equations Type of Bridge a ( × 10 –2 ) b Standard Deviation (1) α ( × 10 –4 ) β ( × 10 –2 ) γ Standard Deviation (2) Year No. of Data Correlation Coefficient Fig. No. Simple plate girder 0.5866 0.0124 0.0325 0.4621 0.2075 0.0881 0.0324 1989–1993 189 0.758 54.3a Simple plate girder (steel deck) 0.3504 0.2499 0.0420 0.1228 –0.5853 0.4252 0.0419 1978–1993 118 0.353 54.3b Simple composite plate girder 0.6084 –0.0306 0.0249 0.3824 0.2985 0.0307 0.0249 1989–1993 383 0.830 54.4 Simple box girder 0.5917 0.0778 0.0410 0.4350 0.1488 0.1866 0.0409 1989–1993 187 0.803 54.5a Simple box girder (steel deck) 0.3019 0.2738 0.0709 0.0616 0.2303 0.2930 0.0709 1978–1993 200 0.556 54.5b Simple composite box girder 0.4765 0.1007 0.0412 0.3329 0.1290 0.1887 0.0411 1981–1993 171 0.714 54.6 Continuous plate girder 0.3729 0.0533 0.0331 –0.3092 0.6425 –0.0035 0.0330 1991–1993 477 0.653 54.7a Continuous plate girder (steel deck) 0.2329 0.2464 0.0484 –0.2413 0.4482 0.2022 0.0481 1978–1993 54 0.508 54.7b Continuous box girder 0.3029 0.1510 0.0499 0.0099 0.2906 0.1546 0.0499 1989–1993 382 0.665 54.8a Continuous box girder (steel deck) 0.1516 0.3110 0.0634 0.0213 0.1080 0.3307 0.0633 1978–1993 337 0.593 54.8b Simple truss 0.2993 0.1421 0.0504 0.3711 –0.2355 0.3284 0.0493 1978–1993 211 0.592 54.9a Continuous truss 0.2221 0.1633 0.0602 0.0959 0.4830 0.0257 0.0567 1978–1993 124 0.799 54.9b Langer 0.2907 0.1433 0.0632 –0.0135 0.3140 0.1338 0.0632 1978–1993 134 0.675 54.10a Trussed Langer 0.2696 0.1700 0.0609 0.1693 –0.1173 0.3794 0.0592 1978–1993 47 0,741 54.10b Lohse 0.2372 0.1956 0.0942 0.0110 0.2128 0.2076 0.0941 1978–1993 183 0.676 54.11a Nielsen Lohse 0.2372 0.1956 0.1019 0.0110 0.2128 0.2076 0.1018 1978–1993 53 0.735 54.11b Rigid frame (Rahmen) 0.4326 0.0542 0.0737 0.4399 –0.1004 0.2024 0.0711 1978–1993 182 0.659 54.14a Rigid frame ( π type) 0.4982 0.0050 0.0555 0.2477 0.1528 0.1160 0.0544 1978–1993 83 0.813 54.14b Cable-stayed bridge (steel deck) 0.2102 0.2944 0.2056 0.0407 –0.0014 0.4736 0.1937 1978–1993 48 0.784 54.15 Equations (tf/m 2 ) aL + b … (1) α L 2 + β L + γ … (2) L = span (m) © 2000 by CRC Press LLC © 2000 by CRC Press LLC FIGURE 54.3 Simple noncomposite plate girders. (a) RC slab deck; (b) steel deck. © 2000 by CRC Press LLC 54.4.2 Simply Supported Composite Plate Girder Bridges The distribution for a simply supported composite plate girder bridge is shown in Figure 54.4. Since many bridges of this type were constructed every year, only 4 years of data are used (1989 to 1993). FIGURE 54.4 Simple composite plate girders. © 2000 by CRC Press LLC 54.4.3 Simply Supported Box-Girder Bridges The distribution for a simply supported box-girder bridge (noncomposite) for RC slab and steel decks is plotted in Figure 54.5. Steel deck bridges show more variation than RC deck bridges. A simply supported composite box-girder bridge is plotted in Figure 54.6. FIGURE 54.5 Simple noncomposite box girders. (a) RC slab deck; (b) steel deck. [...]... values the steel weight of a similar bridge can be estimated FIGURE 54.22 Two-girder bridge in continuous bridges 54.8 Summary The steel weight of bridges is a general indication of the design which tells an overall result It reflects every influential design factor A database has been put together to allow assessment of designs and prediction for the steel weight of various types of highway bridges The... types of framed bridges are compared in Figure 54.18 The Nielsen bridge is the heaviest The Nielsen and Lohse bridges, as well as the trussed Langer, are best suited to long spans FIGURE 54.18 © 2000 by CRC Press LLC Comparison of framed bridges 54.6.4 RC Slab Deck and Steel Deck Figure 54.19a shows a comparison between the mean values of plate girder bridges with RC slab and steel decks Bridges with steel. .. December 1996 [in Japanese] 2 Japan Road Association (JRA), Specifications for Highway Bridges, Vol 1 Common Part, February 1990 [in Japanese] 3 Japan Association of Steel Bridge Construction (JASBC), Annual Report of Steel Bridge Construction, 1978 to 1993 [in Japanese] 4 Toma, S and Honda, Y., Database of steel weight for highway bridges, Bridge Eng., 29(8), 1993 [in Japanese] © 2000 by CRC Press LLC ... shown are for bridges with RC slab and steel decks It is judged that continuous girders are more advantageous when the spans are long There is no significant difference between simple plate and box girders for steel deck bridges Continuous box girders can be used in longspan bridges FIGURE 54.17 © 2000 by CRC Press LLC Comparison of girder bridges (a) RC slab deck; (b) steel deck 54.6.3 Framed Bridges Six... type of bridge From the figures, comparisons are made from various points of view to see the differences in each type of bridge The regression equations for mean weight are derived, from which designers can estimate the steel weight for their own design or see economical or safety features of the bridge as compared with others References 1 Japan Road Association (JRA), Specifications for Highway Bridges, ... Classification of distribution The deviation (H) of the designed steel weight (X) is obtained using the equation H= X − X ( L) × 10 + 50 σ (54.1) H can be used as an index to compare the designs statistically and perform simple assessments of designs © 2000 by CRC Press LLC 54.7.2 Assessment of Design An example assessment of a typical design is discussed in the following The labor and maintenance cost of bridges. .. Continuous box girders (a) RC slab deck; (b) steel deck 54.4.6 Truss Bridges Figure 54.9 is for simply and continuously supported truss bridges The data cluster at moderate span length making prediction for the weight of truss bridges for short or long spans not accurate FIGURE 54.9 © 2000 by CRC Press LLC Truss bridges (a) Simple truss; (b) continuous truss 54.4.7 Arch Bridges Figures 54.10 and 54.11 are... 54.4.4 Continuously Supported Plate Girder Bridges Recently, continuous bridges are gaining popularity as defects caused by expansion joints are avoided Steel weights for continuous bridges with RC slab deck (noncomposite) constructed in the 3 years 1991 to 1993 and with steel deck constructed in the 15 years 1978 to 1993 are plotted in Figure 54.7 The steel deck has only few data and shows wide scatter... Continuous plate girders (a) RC slab deck; (b) steel deck 54.4.5 Continuously Supported Box-Girder Bridges Figure 54.8 shows the distribution for a continuous box-girder bridge with RC slab deck and steel deck This type has a relatively wide scatter It can be seen that the applicable span length of steel deck bridges (Figure 54.8b) is much longer than RC slab deck bridges (Figure 54.8a) FIGURE 54.8 © 2000... 1995-96, JSCE) © 2000 by CRC Press LLC The steel weight of this bridge is plotted in Figure 54.22 The deviation in this case is H = 62.8 (Rank B) using Eq (54.1) In the calculation, the mean and the standard deviations are shown in Table 54.2 Note that most of the continuous bridges in Figure 54.22 are three-span continuous bridges In addition, the design of this bridge follows the new code [1] Those . 54 Statistics of Steel Weight of Highway Bridges 54.1 Introduction 54.2 Design Criteria Live Loads • Materials 54.3 Database of Steel Weights 54.4 Statistics of Steel Weights Simply. " ;Statistics of Steel Weight of Highway Bridges. " Bridge Engineering Handbook. Ed. Wai-Fah Chen and Lian Duan Boca Raton: CRC Press, 2000 © 2000 by CRC Press LLC 54 Statistics of. interest to engineers. Steel weight of highway bridges is one of the most important of the many factors that influence bridge construction projects. The weight gives a good indication of structural, economic,